The flow of a Rivlin-Ericksen fluid in a waving channel

The Flow of a Rivlin-Ericksen Fluid in a Waving Channel Analysis of forced convection and mass transfer in Laminar flow inside a conduit has been the subject of extensive study. Hydrodynamic solutions on steady laminar flow with moderate Reynolds numbers in conduits with irregular surfaces are obtained. In these surfaces the spread of roughness has been large, compared with the mean radius of the conduit. These results are of considerable interest, especially for blood flow in arteries with stenoses and for membrane Oxygenators using parallel plates with wavy surfaces. In this thesis, the fluid model is taken to be Rivlin-Ericksen which is a non-Newtonian fluid. To give an idea, some non-Newtonian effects are summarized below. One of the most important non-Newtonian effects is that viscosity changes due to the change in the velocity field and normal stress differences affects the motion of the fluid. A series of experiments are made to see these effects. Some of these are tube flow where shear thinning or shear thickening occurs; rod climbing where the non-Newtonian Liquid shows the Weissenberg effect ; extrudate swell where a non-Newtonian liquid shows diameter increase upon emergence from the capillary tube? occurrence of secondary flows in the disk and cylinder system; the tubeless siphon; the uebler effect and flow through a sudden contraction. In this study the steady flow of a Rivlin-Ericksen fluid in a channel with waving surfaces is investigated. The fluid is incompressible, the flow is two dimensional and body forces are negligible. It differs from Sturges' work in the way that Sturges' study is unsteady and is investigated only for sinusoidal boundary. In our study, the boundary function can vary so that the problem can be solved for different forms of the boundary, and the problem is taken into account for steady motion. The geometry of the flow is shown below. &- Ay* 11**!In our study the boundary of the channel is given by, n+ (x*) = d(l-eh(x*)), n* (x*) s-da + ehCx*) ) Here h (x ) is chosen as a sinusoidal function. The wavelength is shown to be 2H£. Keyword: Akışkanlar = Fluids ; Kanal modelleri = Channel models ; Rivlin-Ericksen akışkanı = Rivlin-Ericksen fluid